How can the number 301 be expressed using powers of ten?

• A. 3 × 10² + 2
• B. 30 × 10 + 1
• C. 3 × 10² + 1
• D. 3 × 10 + 1

Answer: (C)

To express the number 301 using powers of ten, it's important to break the number down into its component parts based on its place values.

The number 301 can be separated into:

• The hundreds place, which contains the digit 3. This digit represents 300, or (3 \times 10^2).

• The tens place, which contains the digit 0, meaning there are no tens to add.

• The ones place, which has the digit 1, representing (1) or (1 \times 10^0).

When we add these parts together, we get:

[

301 = 3 \times 10^2 + 0 \times 10^1 + 1 \times 10^0

]

Since the tens place contributes zero, it does not need to be included in the expression. Thus, we can write:

[

301 = 3 \times 10^2 + 1

]

This correctly captures the value of 301 using powers of ten, making it clear why the chosen answer is valid. It emphasizes the significance of each digit's placement in the overall value of the number.